Place a medium saucepan over medium heat. Add the chopped figs, 2 tablespoons olive oil, onion, and shallot. Stir and cook until the onions are soft and beginning to brown at the edges, about 5 to 7 minutes. Add the sugar, vinegar, vegetable broth, salt, and pepper. Bring the liquid to a boil, reduce the heat, and simmer, covered, for 30 minutes. Remove the cover and continue simmering until most of the liquid is reduced and the mixture is the consistency of jam, about 30 minutes. Remove from the heat and set aside.
Combine 2 tablespoons olive oil, grapes, olives, and rosemary in a baking dish. Roast in oven until skins become soft and grapes and olives release much of their juices, about 30 minutes. Remove from the oven, let cool slightly, then pulse lightly in a food processor. Fold into cooled fig jam.
Serve on chicken, lamb, or crostini. Store in an airtight container in the refrigerator for 2 to 3 weeks.
Recipe by Allons-Eat! at https://www.allonseat.com/fig-olive-and-roasted-grape-jam/